A Unified Analytical Look at Reynolds Flocking Rules

In this paper, we present a unified theoretical view of the so-called “Flocking Rules of Reynolds” introduced in 1987. No equations describing the rules or mathematical models of the mobile agents known as “boids” were presented in the original work by Reynolds. We show how to model a group of autonomous mobile agents by dynamic nets and achieve flocking by dissipation of the structural energy of the multi-agent system. As a by-product, we obtain a single protocol called the (α, α) protocol that encompasses all three flocking rules of Reynolds. We provide geometric interpretations of the advanced forms of some of these flocking rules. Simulation results are provided that demonstrate flocking of 100 agents towards a sink.